SetDelayed¶

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description¶

lhs := rhs or SetDelayed[lhs, rhs]
    assigns rhs to lhs as a delayed rule: rhs is held and evaluated
    each time the rule fires (with bindings from lhs substituted in),
    not at assignment time.  SetDelayed has attribute HoldAll.

Examples¶

No verified examples yet for this function.

Implementation notes¶

Algorithm. SetDelayed (:=) shares the special-primitive path with Set in evaluate_step (src/eval.c, step 6, head_name == SYM_SetDelayed). The head carries ATTR_HOLDALL (src/attr.c), so neither side is pre-evaluated: the RHS is stored unevaluated and re-evaluated each time the rule fires. As with Set, the LHS is partially evaluated to canonicalise the assignment target (arguments evaluated, head and pattern-bearing/destructuring sub-elements held — see lhs_arg_contains_pattern), then apply_assignment(lhs, rhs, is_delayed=true) installs the value. SetDelayed returns the symbol Null rather than the RHS.

Data structures. Symbol LHS → OwnValue (symtab_add_own_value); function-head LHS → DownValue (symtab_add_down_value) keyed on the head, with the full LHS as the match pattern and the held RHS as the replacement; List LHS recurses for destructuring. One delayed-specific transform: if the RHS is Condition[body, test], apply_assignment rewrites the rule as Condition[lhs, test] := body, so f[x_] := body /; test is stored equivalently to f[x_] /; test := body; the condition's head symbol is then unwrapped to find the true DownValue key. Protected targets are refused with a SetDelayed::wrsym message. For $RecursionLimit a copy of the RHS is evaluated to sync the C-side limit.

Attributes: HoldAll, Protected.

Implementation status¶

Stable — documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

References¶

Source: src/eval.c
Specification: docs/spec/builtins/assignment-and-rules.md

Notes & additional examples¶

Worked examples¶

In[1]:= f[n_] := n^2
Out[1]= Null

In[2]:= f[4]
Out[2]= 16

In[3]:= f[a + b]
Out[3]= (a + b)^2

Notes¶

:= (SetDelayed) holds the right-hand side and re-evaluates it each time the rule fires, with the pattern bindings substituted in. The definition itself returns Null.